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Physics LibreTexts

8: Sparse Matrices

( \newcommand{\kernel}{\mathrm{null}\,}\)

A sparse matrix is a matrix in which most of the entries are zero. Such matrices are very commonly encountered in finite-difference equations. For example, when we discretized the 1D Schrödinger wave equation with Dirichlet boundary conditions, we saw that the Hamiltonian matrix had the tridiagonal form

H=12h2[2112112]+[V0V1VN1].

Hence, if there are N diagonalization points, the Hamiltonian matrix has a total of N2 entries, but only O(N) of these entries are non-zero.


This page titled 8: Sparse Matrices is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Y. D. Chong via source content that was edited to the style and standards of the LibreTexts platform.

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